How to better confine and manipulate light has always been an important research topic in optics. Resonant states in optical fibers or photonic crystals are typical designs for confining light, but due to the existence of leakage, the light confinement in these ways is not perfect, and light transmission in these structures will inevitably cause loss. As the loss generation will reduce the interaction efficiency between light and matter, a new method is needed to confine light more effectively and further reduce the loss. The bound state in the continuum (BIC) is a special eigenstate different from the extended state and leaky state in the continuum. It is located in the frequency range of the continuum with strong locality and does not radiate energy into free space. In 1929, von Neumann and Wigner built a mathematical model of artificial potential and discovered the existence of BIC for the first time. After that, BIC research has been vigorously developed, and the existence of BIC has been found in the fields of electromagnetics, nuclear physics, and acoustics. In 1985, Friedrich and Wintgen proposed a method to construct BIC. By adjusting the structural parameters, the eigenstates are coupled at the same position to make the loss of one eigenstate close to 0, and it is transformed into a BIC. The BIC generated by this method is also called Friedrich-Wintgen BIC. Fabry-Pérot BIC occurs when two eigenstates are not coupled at the same location. Designed optical structures can generate BIC, and these structures are usually periodic. By adjusting the structural parameters and material properties, BIC of specific frequency can be generated. For example, metasurfaces and plasmons are commonly employed structures to realize BIC. In 2011, Plotnik et al. adopted one-dimensional optical waveguide to observe the symmetrically protected BIC in the experiment for the first time.

Optical BIC has two important advantages, including the near-infinite quality factor and the ability to generate far-field vortex singularities. These properties help generate sharp resonances with high quality factors in subwavelength-scale optical structures and can emit vortex light without the help of three-dimensional structures. This is conducive to constructing ultra-thin integrated optical components in the future, and enhancing the interaction between light and matter (such as nonlinear effects and quantum effects), with important potential in optical imaging and information transmission. Therefore, BIC has become a popular research direction in photonics and is studied in various photonic systems such as photonic crystals, metasurfaces, and plasmons.

This paper first introduces the taxonomy of photonics BICs. According to the differences with the far-field decoupling method, it is divided into two types of symmetry-protected BIC (Fig. 1) and accidental BIC (Fig. 2). Symmetry-protected BIC originates from symmetry mismatch, and accidental BIC originates from far-field interference cancellation of radiation components. Accidental BIC is divided into Fabry-Pérot BIC, Friedrich-Wintgen BIC, and single-resonance BIC according to the different radiation channels producing interference destructiveness. Fabry-Pérot BIC is produced by the coupling of two modes at different positions, Friedrich-Wintgen BIC by the coupling of two modes at the same position, and single resonance BIC by the coupling of different waves in the same mode. Then several commonly utilized theoretical models for explaining BIC are introduced (Fig. 3), including energy band theory, temporal coupled-mode theory, and multipole analysis. These theoretical models provide different perspectives to explain the physical mechanisms of BIC. Finally, the existing applications of BIC in photonics are introduced. For example, BIC is employed to enhance the nonlinear effect to realize laser emission and high-order harmonic generation (Fig. 4). Polarization control and chirality enhancement are realized by exploiting the vortex singularity properties of BIC (Fig. 5). Filtering and sensing are performed with the help of the sharp resonance peak characteristics of BIC with high quality factors (Fig. 6). Additionally, since BIC in the optical waveguide can realize efficient optical signal transmission, they are of application significance in photonic integrated circuits (Fig. 7).

In summary, due to their ability to greatly enhance the interaction between light and matter, and control the outgoing light with extremely low energy loss, BIC has been studied in many optics fields, and various theoretical models for interpreting BIC generation have also been continuously developed and improved. At this stage, BIC still has bottlenecks such as difficult structure processing and design, and is expected to gradually make breakthroughs in the future.